A resistor develops 800 J of thermal energy in 20 s on applying a potential difference of 20 V. Its resistance is

The correct option is 10 Ω.

Let us understand how to arrive at this result step-by-step using the principles of electrical physics.

Step 1: Identify the given values
We are given the following values in the problem:
- Thermal energy developed ($H$) = 800 J
- Time interval ($t$) = 20 s
- Potential difference ($V$) = 20 V

Step 2: Understand the formula relating energy, voltage, time, and resistance
According to Joule's law of heating, the thermal energy ($H$) developed in a resistor of resistance $R$ when a potential difference $V$ is applied across it for a time $t$ is given by the formula:
$H=\frac{V^2}{R}·t$
Here, $H$ represents the heat or thermal energy in Joules (J), $V$ represents the potential difference in Volts (V), $t$ represents the time in seconds (s), and $R$ represents the electrical resistance in Ohms (Ω).

Step 3: Rearrange the formula to solve for Resistance ($R$)
To find the resistance, we rearrange the terms in the formula:
$R=\frac{V^2}{H}·t$

Step 4: Substitute the given values into the rearranged formula
Now we insert the given values into the equation:
$R=\frac{{\left(20\right)}^2}{800}·20$
First, calculate the square of the potential difference:
${20}^2=400$
Now, substitute this back into the expression:
$R=\frac{400}{800}·20$
Simplify the fraction:
$\frac{400}{800}=0.5$
Finally, multiply by the time:
$R=0.5·20=10\Omega$

Thus, the resistance of the resistor is 10 Ω.